Tensor Spaces And Exterior Algebra PDF Download
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Author | : Takeo Yokonuma |
Publisher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 9780821827963 |
Download Tensor Spaces and Exterior Algebra Book in PDF, ePub and Kindle
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
Author | : Sergei Winitzki |
Publisher | : Sergei Winitzki |
Total Pages | : 286 |
Release | : 2009-07-30 |
Genre | : Science |
ISBN | : 140929496X |
Download Linear Algebra Via Exterior Products Book in PDF, ePub and Kindle
This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Author | : J. M. Landsberg |
Publisher | : American Mathematical Soc. |
Total Pages | : 464 |
Release | : 2011-12-14 |
Genre | : Mathematics |
ISBN | : 0821869078 |
Download Tensors: Geometry and Applications Book in PDF, ePub and Kindle
Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.
Author | : Katsumi Nomizu |
Publisher | : |
Total Pages | : 190 |
Release | : 1961 |
Genre | : Calculus of tensors |
ISBN | : |
Download Vector Spaces and Tensor Algebras Book in PDF, ePub and Kindle
Author | : Hongyu Guo |
Publisher | : World Scientific |
Total Pages | : 246 |
Release | : 2021-06-16 |
Genre | : Mathematics |
ISBN | : 9811241031 |
Download What Are Tensors Exactly? Book in PDF, ePub and Kindle
Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Author | : Paul Renteln |
Publisher | : Cambridge University Press |
Total Pages | : 343 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 1107042194 |
Download Manifolds, Tensors and Forms Book in PDF, ePub and Kindle
Comprehensive treatment of the essentials of modern differential geometry and topology for graduate students in mathematics and the physical sciences.
Author | : Adam Marsh |
Publisher | : World Scientific |
Total Pages | : 301 |
Release | : 2017-11-27 |
Genre | : Science |
ISBN | : 9813233931 |
Download Mathematics For Physics: An Illustrated Handbook Book in PDF, ePub and Kindle
This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.
Author | : Wolfgang Hackbusch |
Publisher | : Springer Science & Business Media |
Total Pages | : 525 |
Release | : 2012-02-23 |
Genre | : Mathematics |
ISBN | : 3642280277 |
Download Tensor Spaces and Numerical Tensor Calculus Book in PDF, ePub and Kindle
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.
Author | : Paolo Aluffi |
Publisher | : American Mathematical Soc. |
Total Pages | : 713 |
Release | : 2021-11-09 |
Genre | : Education |
ISBN | : 147046571X |
Download Algebra: Chapter 0 Book in PDF, ePub and Kindle
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author | : Jorge Stolfi |
Publisher | : Academic Press |
Total Pages | : 246 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483265196 |
Download Oriented Projective Geometry Book in PDF, ePub and Kindle
Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.